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Critical load for buckling

  1. Jun 28, 2011 #1
    1. The problem statement, all variables and given/known data
    A rod of leangth L and flexural rigidity EI is pinned at one end by means of torsional spring having a constant beta, and fixed on the other end.
    The rod is subjected to a compressive axial force P.
    Determine the critical load for instability.(image of the problem is attached)

    2. Relevant equations
    As far as I understand, the way to solve this problem is:
    M(x)=-R*x-P*v(x)+beta*v'(0) , where R is the reaction on the left end at the y direction v(x) is the deflection function and v'(x) is the angle function.
    M(x)=v''(x)*IE
    3. The attempt at a solution

    the two equations above yields:
    v''(x)+(P/EI)*v(x)= (beta*v'(0)-R*x)/EI ->

    v(x)=A*sin(sqrt(P/EI)*x)+B*cos(sqrt(P/EI)*x)+beta*v'(0)-R*x

    to find those constants the boundry conditions are: v(o)=0 v(L)=0 v'(L)=0

    How do I represent v'(0) which is unknown ?
     

    Attached Files:

  2. jcsd
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